Electric birefringence in Euler-Heisenberg pseudo-electrodynamics

The fermion sector of the pseudo-quantum electrodynamics is integrated functionally to generate a non-linear electrodynamics, that it is called Euler-Heisenberg pseudo-electrodynamics. A non-local Chern-Simons topological term is added to the original lagrangian of the pseudo-quantum electrodynamics in which a most complete electrodynamics gauge invariant in 1+2 dimensions is proposed. As consequence of the fermionic sector, we obtain a non-linear contribution in the electromagnetic fields that breaks the Lorentz symmetry due to Fermi velocity. From the Euler-Heisenberg pseudo-electrodynamics, we study the properties of the plane wave propagating in a planar medium under an uniform and constant electromagnetic background field. The properties of the planar material are discussed through the electric permittivity tensor and magnetic permeability, that are functions of the frequency, wavelength and of the background fields. The dispersion relations and the refractive index are calculated in the presence of a uniform magnetic field, and also in the case only of an electric background field. The birefringence phenomenon emerges only when the electric background field is considered.

💡 Research Summary

The paper introduces a novel non‑linear electrodynamics in (2+1)‑dimensional space‑time, called Euler‑Heisenberg pseudo‑electrodynamics (EHPED), which arises from integrating out massive Dirac fermions coupled to pseudo‑quantum electrodynamics (PQED). PQED itself is a non‑local Abelian gauge theory obtained by confining the usual Maxwell sources to a planar sheet, leading to a kinetic term proportional to (F_{\mu\nu}, \Box^{-1/2} F^{\mu\nu}). The authors augment this gauge sector with a non‑local Chern‑Simons (CS) term (\theta,\epsilon^{\mu\nu\rho} A_\mu \Box^{-1/2}\partial_\nu A_\rho), preserving gauge invariance while introducing a topological mass‑like parameter (\theta).

Starting from the Lagrangian \